Geodesic
An improved upper bound on the growth constant of polyiamonds
Gill Barequet1 ; Guenter Rote2 ; Mira Shalah3 ; Gill Barequet ; Guenter Rote ; Mira Shalah
1Dept. of Computer Science, Technion - Israel Inst.of Technology, Haifa, Israel
2Institut für Informatik, Freie Universität Berlin, Berlin, Germany
3Dept. of Computer Science, Stanford University, Stanford, USA
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 429-436 
Gill Barequet; Guenter Rote; Mira Shalah; Gill Barequet; Guenter Rote; Mira Shalah. An improved upper bound on the growth constant of polyiamonds. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 429-436. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a11/
@article{AMUC_2019_88_3_a11,
     author = {Gill Barequet and Guenter Rote and Mira Shalah and Gill Barequet and Guenter Rote and Mira Shalah},
     title = { An improved upper bound on the growth constant of polyiamonds},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {429--436},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a11/}
}
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Voir la notice de l'article provenant de la source Comenius University

A polyiamond is an edge-connected set of cells on the triangular lattice. Let~$T(n)$ denote the number of distinct (up to translation) polyiamonds made of~$n$ cells. It is known that the sequence~$T(n)$ has an asymptotic growth constant, i.e., the limit $\lambda_T := \lim_{n \to \infty} T(n+1) / T(n)$ exists, but the exact value of~$\lambda_T$ is still unknown. In this paper, we improve considerably the best known upper bound on~$\lambda_T$ from~4 to~3.6108.